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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m/s and the second part of mass 2 kg moves with speed 8 m/s. If the third part flies off with speed 4 m/s, its mass is:

1. 5 kg
2. 7 kg
3. 17 kg
4. 3 kg

Correct answer: 5 kg

Solution

Using the law of conservation of momentum, the total momentum before and after the explosion must be equal. Since the rock was initially at rest, the total momentum in both x and y directions must be zero. Solving for the third mass using vector components, we find it to be 5 kg.

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